notes/29-Nov.org


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Jacobi Iteration (cont.)

x^{k+1} = D^{-1}(b - (L + U)x^k)

{
  x^{k+1} = x^k + D^-1 r^k
  r^{k} = b - Ax^k
}

error: || x^{k+1} - x^k ||_2
residual: || r^k ||_2

Gauss-Seidel Iteration:
A = (L + D + U)
\Rightarrow Ax = b
  (D + U)x = b - Lx
  x = (D + U)^-1 (b - Lx)

x^{k+1} = (D+U)^{-1}(b - Lx^k)
(D + U)^{-1} x (bsubst)